One of the treatments for Parkinson’s disease in some patients is Deep Brain Stimulation (DBS) (Davidson, 2012). In DBS a set of electrodes is surgically implanted and a vibrating current is applied to the subthalamic nucleus, also known as a brain pacemaker. Root locus has been used on a linearized model of the system to help explain the dynamics of DBS. The DBS model can be obtained by substituting
in the unity-feedback diagram of Figure P8.3.
a. Make a sketch of the resulting root locus as a function of k and find the break-in point and its corresponding value of gain.
b. Find the range of k for closed-loop stability in terms of b.
c. Find the frequency of oscillation when the system has closed-loop poles on the jω axis.
